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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Confidence Intervals"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In a previous coin-flipping discussion, we discussed estimation of the underlying probability of getting a heads. There, we derived the estimator as \n",
      "\n",
      "$$ \\hat{p}_n = \\frac{1}{n}\\sum_{i=1}^n X_i $$\n",
      "\n",
      "Confidence intervals allow us to estimate how close we can get to the true value that we are estimating. Logically, that seems strange, doesn't it? We really don't know the exact value of what we are estimating (otherwise, why estimate it?), and yet, somehow we know how close we can get to something we admit we don't know? Ultimately, we want to make statements like the \"probability of the value in a  certain interval is 90%\". Unfortunately, that is something we will not be able to say using our methods. Note that Bayesian estimation gets closer to this statement by using \"credible intervals\", but that is a story for another day. In our situation, the best we can do is say roughly the following: \"if we ran the experiment multiple times, then the confidence interval would trap the true parameter 90% of the time\".\n",
      "\n",
      "Let's return to our coin-flipping example and see this in action. One way to get at a confidence interval is to use Hoeffding's inequality specialized to our Bernoulli variables as \n",
      "\n",
      "$$ \\mathbb{P}(|\\hat{p}_n-p|>\\epsilon) \\le 2 \\exp(-2n \\epsilon^2) $$ \n",
      "\n",
      "Now, we can form the interval $\\mathbb{I}=[\\hat{p}_n-\\epsilon_n,\\hat{p}_n+\\epsilon_n]$, where $\\epsilon_n$ is carefully constructed as\n",
      "\n",
      "$$ \\epsilon_n = \\sqrt{ \\frac{1}{2 n}\\log\\frac{2}{\\alpha}}$$\n",
      "\n",
      "which makes the right-side of the Hoeffding inequality equal to $\\alpha$. Thus, we finally have\n",
      "\n",
      "$$ \\mathbb{P}(p \\notin \\mathbb{I}) = \\mathbb{P}(|\\hat{p}_n-p|>\\epsilon_n) \\le \\alpha$$\n",
      "\n",
      "Thus, $ \\mathbb{P}(p \\in \\mathbb{I}) \\ge 1-\\alpha$. As a numerical example, let's take $n=100$, $\\alpha=0.05$, then plugging into everything we have gives $\\epsilon_n=0.136$. So, the 95% confidence interval here is therefore\n",
      "\n",
      "$$\\mathbb{I}=[\\hat{p}_n-\\epsilon_n,\\hat{p}_n+\\epsilon_n] = [\\hat{p}_n-0.136,\\hat{p}_n+0.136]$$\n",
      "\n",
      "The following code sample is a simulation to see if we can really trap the underlying parameter in our confidence interval."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import stats\n",
      "from scipy.stats import  bernoulli\n",
      "b=bernoulli(.5) # fair coin distribution\n",
      "nsamples = 100\n",
      "xs = b.rvs(nsamples*200).reshape(nsamples,-1) # flip it nsamples times for 200 estimates\n",
      "phat = mean(xs,axis=0) # estimated p\n",
      "epsilon_n=sqrt(np.log(2/0.05)/2/nsamples) # edge of 95% confidence interval\n",
      "print '--Interval trapped correct value ',np.logical_and(phat-epsilon_n<=0.5, 0.5 <= (epsilon_n +phat)).mean()*100,'% of the time'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "--Interval trapped correct value  100.0 % of the time\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The result in the previous cell shows that the estimator and the corresponding interval was able to trap the true value at least 95% of the time. This is how to interpret the action of confidence intervals.\n",
      "\n",
      "However, the usual practice is to not use Hoeffding's inequality and instead use arguments around asymptotic normality. First, we need a concept of what *asymptotic* means."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Types of Convergence"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's consider the following sequences of random variables where $X_n = 1/2^n$ with probability $p_n$ and where $X_n=c$ with probability $1-p_n$. Then, we have $X_n  \\overset{P}{\\to} 0$ as $p_n \\rightarrow 1$. This is allowable under this notion of convergence because a diminishing amount of *non-converging* behavior (namely, when $X_n=c$) is possible. Note that we have said nothing about *how* $p_n \\rightarrow 1$.\n",
      "\n",
      "Now, let's consider the convergence in distribution case. Suppose we have $X_n \\sim \\mathcal{N}(0,1/n)$, which means that the variance for each of the $X_n$ gets smaller and smaller. By a quick change of variables, this means that $Z=\\sqrt{n}X_n \\sim \\mathcal{N}(0,1)$. For $t<0$ we have the following:\n",
      "\n",
      "$$ F_n(t) = \\mathbb{P}(X_n<t) =\\mathbb{P}(Z<\\sqrt{n}t) \\rightarrow 0$$\n",
      "\n",
      "as $n\\rightarrow \\infty$. Likewise, for $t>0$, we have $ F_n(t) = \\mathbb{P}(X_n<t) \\rightarrow 1 $ as $n\\rightarrow \\infty$.\n",
      "\n",
      "Hence, $F_n(t) \\rightarrow F(t)$ where $t\\neq0$. What about $F_n(1/2)=1/2$ where $F(1/2)=1$? Convergence has failed for this point, but that does not matter for this definition of convergence because we only need convergence at the continuity points of $F(t)$.\n",
      "\n",
      "The main thing to keep in mind about convergence in probability versus convergence in distribution is that the former is concerned about the random variables themselves whereas the latter is only about their corresponding distribution functions. This implies that for convergence in distribution, the random variables do not even have to exist in the same space or have a (function-wise) limit in the same space. This is not true for convergence in probability, which is thereby more restrictive."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Up to this point, we have been intuitively using some ideas about convergence that we now have to nail down. The first kind of convergence is *convergence in probability* which means the following:\n",
      "\n",
      "$$ \\mathbb{P}(|X_n -X|> \\epsilon) \\rightarrow 0$$\n",
      "\n",
      "as $n \\rightarrow 0$. This is notationally shown as $X_n  \\overset{P}{\\to} X$.\n",
      "\n",
      "The second major kind of convergence is *convergence in distribution* where\n",
      "\n",
      "$$ \\lim_{n \\to \\infty}  F_n(t) = F(t)$$\n",
      "\n",
      "for all $t$ for which $F$ is continuous. Bear in mind that we are talking about $F(t)$ as the probability cumulative density for $X$. This kind of convergence is usually annotated as $X_n \\rightsquigarrow X$. \n",
      "\n",
      "The third and final convergence we are interested in is *quadratic mean convergence* where\n",
      "\n",
      "$$ \\lim_{n\\rightarrow 0} \\mathbb{E}(X_n-X)^2 \\rightarrow 0 $$\n",
      "\n",
      "This is notationally shown as $X_n  \\overset{qm}{\\to} X$. These forms of convergence form a hierarchy where quadratic mean convergence implies convergence in probability, which in turn, implies convergence in distribution. Except in certain special cases, this hierarchy is rigid. It turns out we need these notions in order to collect a wide range of useful results that derive from each of these categories in turn. Here is a concrete example that illustrates the different kinds of convergence. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This finally leads us to the idea of the *weak law of large numbers*: If $X_i$ are all independent, identically-distributed with mean $\\mu=\\mathbb{E}(X_1)$, then\n",
      "\n",
      "$$ \\bar{X_n} \\overset{P}{\\to} \\mu$$\n",
      "\n",
      "It turns out that many useful estimators are asymptotically normal:\n",
      "\n",
      "$$ \\frac{\\hat{\\theta_n}-\\theta}{\\texttt{se}} \\rightsquigarrow \\mathcal{N}(0,1)$$\n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Back to confidence intervals"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The definition of the standard error is the following:\n",
      "\n",
      "$$ \\texttt{se} = \\sqrt{\\mathbb{V(\\hat{\\theta}_n)}}$$\n",
      "\n",
      "where $\\hat{\\theta}_n$ is the point-estimator for the parameter $\\theta$, given $n$ samples of data $X_n$. The $\\mathbb{V}$ is the variance of $\\hat{\\theta}_n$. Likewise, the estimated standard error is $\\hat{\\texttt{se}}$. For example, in our coin-flipping example, the estimator was $\\hat{p}=\\sum X_i/n$ with corresponding variance $\\mathbb{V}(\\hat{p}_n)=p(1-p)/n$\n",
      "\n",
      "we are plugging in a point estimate into a formula for the variance of $\\theta$. This gives us the estimated standard error: $\\hat{\\texttt{se}}=\\sqrt{\\hat{p}(1-\\hat{p})/n}$\n",
      "\n",
      "From the result above, for our coin-flipping example, we know that $\\hat{p}_n \\sim \\mathcal{N}(p,\\widehat{\\texttt{se}}^2)$. Thus, if we want a $1-\\alpha$ confidence interval, we can compute\n",
      "\n",
      "$$ \\mathbb{P}(|\\hat{p}_n-p| \\lt \\xi)\\gt 1-\\alpha$$ \n",
      "\n",
      "but since we know that $ (\\hat{p}_n-p)$ is asymptotic normal, $\\mathcal{N}(0,\\widehat{\\texttt{se}}^2)$, we can instead compute\n",
      "\n",
      "$$ \\int_{-\\xi}^{\\xi} \\mathcal{N}(0,\\widehat{\\texttt{se}}^2) dx \\gt 1-\\alpha$$\n",
      "\n",
      "This looks ugly to compute because we need to find $\\xi$, but `scipy.stats` has everything we need for this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "se=sqrt(phat*(1-phat)/xs.shape[0]) # compute estimated se for all trials\n",
      "rv=stats.norm(0, se[0]) # generate random variable for trial 0\n",
      "array(rv.interval(0.95))+phat[0] # compute 95% confidence interval for that trial 0\n",
      "\n",
      "def compute_CI(i):\n",
      "    return stats.norm.interval(0.95,loc=i,scale=sqrt(i*(1-i)/xs.shape[0]))\n",
      "lower,upper = compute_CI(phat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "fig.set_size_inches((10,3))\n",
      "ax.axis(ymin=0.2,ymax=0.9,xmax=100)\n",
      "ax.plot(upper,label='upper asymptotic',lw=2.)\n",
      "ax.plot(lower,label='lower asymptotic',lw=2.,color='b')\n",
      "ax.plot(phat,'o',color='gray',label='point estimate')\n",
      "ax.plot(phat+epsilon_n,label='Hoeffding upper',color='g')\n",
      "ax.plot(phat-epsilon_n,label='Hoeffding lower',color='g')\n",
      "ax.set_xlabel('trial index')\n",
      "ax.set_ylabel('value of estimate')\n",
      "ax.legend(loc=(1,0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.legend.Legend at 0xc742d90>"
       ]
      },
      {
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       "output_type": "display_data",
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G8+YB69fpoadNzwqduSQinAg5gVF2CgfUuXOB7GzmX7GqyG944kTgsZJ7wBTH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\nIiIiIuJBKuRFRERERDzo/wFQCyOWWQQQOwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc699310>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above figure shows the asymptotic confidence intervals and the Hoeffding-derived confidence intervals. As shown, the Hoeffding intervals are a bit more generous than the asymptotic estimates. However, this is only true so long as the asympotic approximation is valid. In other words, there exists some number of $n$ samples for which the asymptotic intervals may not work. So, even though they may be a bit more generous, the Hoeffding intervals do not require arguments about asymptotic convergence in order to work. In practice, nonetheless, asymptotic convergence  is always in play (even if not explicitly stated)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "xi=linspace(-3,3,100)\n",
      "ax.plot(xi,stats.norm.pdf(xi))\n",
      "ax.fill_between(xi[17:-17],stats.norm.pdf(xi[17:-17]),alpha=.3)\n",
      "ax.text(-1,0.15,'95% probability',fontsize=18)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x76a8f30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yo3nqqXasWfMiXbsOo0qVmnllS3Oznbp1m3DttW3YsmUxzZt3pU+ftowYkU1o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\n7l0ZX98cJk7Um3RfCm3Bu6C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       "text": [
        "<matplotlib.figure.Figure at 0x76a85f0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Confidence Intervals and Hypothesis testing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It turns out that there is a close dual relationship between hypothesis testing and the confidence intervals we have been discussing. To see this in action, consider the following hypothesis test for a normal distribution, $H_0 :\\mu=\\mu_0$ versus $H_1: \\mu \\neq \\mu_0$. A reasonable test has the following rejection region:\n",
      "\n",
      "$$ \\left\\{ x: |\\bar{x}-\\mu_0| \\gt z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n} \\right\\}$$\n",
      "\n",
      "which is the same thing as saying that the region corresponding to acceptance of $H_0$ is then,\n",
      "$$\\bar{x} -z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n}  \\le \\mu_0 \\le \\bar{x} +z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n}$$\n",
      "\n",
      "Because the test has size $\\alpha$, this means that $\\mathbb{P}(H_0 \\, \\texttt{rejected}|\\mu=\\mu_0)=\\alpha$, which is the same thing as saying the probability of *false alarm*. Likewise, the $\\mathbb{P}(H_0 \\, \\texttt{accepted}|\\mu=\\mu_0)=1-\\alpha$. Putting this all together with interval defined above means that \n",
      "\n",
      "$$ \\mathbb{P}\\left(\\bar{x} -z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n}  \\le \\mu_0 \\le \\bar{x} +z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n} \\Big| H_0\\right) =1-\\alpha$$ \n",
      "\n",
      "Because this is valid for any $\\mu_0$, we can drop the $H_0$ condition and say the following:\n",
      "\n",
      "$$ \\mathbb{P}\\left(\\bar{x} -z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n}  \\le \\mu_0 \\le \\bar{x} +z_{\\alpha/2}\\frac{\\sigma}{\\sqrt n} \\right) =1-\\alpha$$\n",
      "\n",
      "As may be obvious by now, the interval above *is* the $1-\\alpha$ confidence interval! Thus, we have just obtained the confidence interval by inverting the acceptance region of the level $\\alpha$ test. The hypothesis test fixes the *parameter* and then asks what sample values (i.e. the acceptance region) are consistent with that fixed value. Alternatively, the confidence interval fixes the sample value and then asks what parameter values (i.e. the confidence interval) make this sample value most plausible. Note that sometimes this inversion method results in disjoint intervals (known as *confidence sets*)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Bootstrap Confidence interval"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# resample with replacement\n",
      "bs=[np.random.choice(xs[:,0],size=len(xs[:,0])).mean() for i in range(100)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use kernel density estimate to approximate empirical PDF\n",
      "from scipy.stats import gaussian_kde\n",
      "kbs=gaussian_kde(bs) # kernel density estimate\n",
      "fig,ax=subplots()\n",
      "ax.hist(bs,20,normed=True,alpha=.3);\n",
      "i=linspace(.25,.7,100)\n",
      "ax.plot(i,kbs.evaluate(i),lw=3.,label='kernel density\\nestimate')\n",
      "ax.vlines(phat[0],0,12,lw=4.,linestyle='--')\n",
      "ax.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.legend.Legend at 0xc92bfb0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PkwvtucqrFgBHc/YTn/lLOUsIcYldR+xKqaHAaa31DqVUTGnzTZ8+3ZiOiYkh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\nCDcjhV0IIdyMFHYhhHAzUtiFEMLN/H/oJ7LyTer8CAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc84b1b0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delta=.1\n",
      "kbs.integrate_box(phat[0]-delta,phat[0]+delta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "0.9453581624419674"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fsolve\n",
      "delta=fsolve(lambda delta:0.95-kbs.integrate_box(phat[0]-delta,phat[0]+delta) ,0.1)[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "ax.hist(bs,20,normed=True,alpha=.3);\n",
      "i=linspace(.25,.95,100)\n",
      "ax.plot(i,kbs.evaluate(i),lw=3.,label='kernel density\\nestimate')\n",
      "ax.vlines(phat[0],0,12,lw=4.,linestyle='--')\n",
      "ax.vlines(phat[0]+delta,0,12,lw=4.,linestyle='--',color='gray')\n",
      "ax.vlines(phat[0]-delta,0,12,lw=4.,linestyle='--',color='gray')\n",
      "ii=i[np.where(logical_and(i < phat[0]+delta ,i>phat[0]-delta ))]\n",
      "ax.fill_between(ii,kbs.evaluate(ii),alpha=.3,color='m')\n",
      "ax.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.legend.Legend at 0xca99cf0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rKeY+4vTZ06TnpwMQqkJJLE8yN5CL2V4E3V+WSlllmYlphPA9Usx9hG2rfGDr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\nhB/4//ifiJORNHPUAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc93d8b0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_bootstrap_CI(x,nboot=100):\n",
      "    phat = x.mean()\n",
      "    bs=[np.random.choice(x,size=len(xs)).mean() for i in range(nboot)]\n",
      "    kbs=gaussian_kde(bs) # kernel density estimate\n",
      "    delta=fsolve(lambda delta:0.95-kbs.integrate_box(phat-delta,phat+delta) ,0.1)[0]\n",
      "    return (phat-delta,phat+delta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute bootstrap confidence intervals\n",
      "upper_b,lower_b=zip(*[ compute_bootstrap_CI(xs[:,i]) for i in range(xs.shape[1]) ])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax=subplots()\n",
      "fig.set_size_inches((10,3))\n",
      "ax.axis(ymin=0.2,ymax=0.9,xmax=100)\n",
      "ax.plot(upper,label='upper asymptotic',lw=2.)\n",
      "ax.plot(lower,label='lower asymptotic',lw=2.,color='b')\n",
      "ax.plot(phat,'o',color='gray',label='point estimate')\n",
      "ax.plot(phat+epsilon_n,label='Hoeffding upper',color='g')\n",
      "ax.plot(phat-epsilon_n,label='Hoeffding lower',color='g')\n",
      "ax.plot(upper_b,label='upper bootstrap',lw=2.,color='m')\n",
      "ax.plot(lower_b,label='lower bootstrap',lw=2.,color='m')\n",
      "ax.set_xlabel('trial index')\n",
      "ax.set_ylabel('value of estimate')\n",
      "ax.legend(loc=(1,0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.legend.Legend at 0xcd83450>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eiEpSMbjNYE4lNOyMOD5hPgxzHcbrf77eoMd9UKgz1By+cphrmmv13jerOAv/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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xca71050>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Medical Example: One-sided vs Two-sided"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# example from Good's \"Common Errors in Statistics\" book p.19 (which is, ironically, wrong)\n",
      "from pandas import DataFrame\n",
      "df=DataFrame(index=('male','female'))\n",
      "df['survived']=(9,4)\n",
      "df['died']=(1,10)\n",
      "df"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>survived</th>\n",
        "      <th>died</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>male</th>\n",
        "      <td> 9</td>\n",
        "      <td>  1</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>female</th>\n",
        "      <td> 4</td>\n",
        "      <td> 10</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "        survived  died\n",
        "male           9     1\n",
        "female         4    10"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above data shows cancer survival rates at a particular hospital. How can we determine whether or not gender has anything to do with survival? For a hypothesis testing process, we could define $H_0$ as the hypothesis that there is no gender difference in survival rates. This is actually kind of tricky to simulate, but we can get at some of the ideas below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import itertools as it\n",
      "import combinatorics # from pypi.org\n",
      "from collections import Counter\n",
      "\n",
      "patients = ['M']*10 + ['F']*14\n",
      "sample= np.random.permutation(patients)[:13] # use the first 13 slots for survivors\n",
      "print sample\n",
      "print Counter(sample)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "['F' 'F' 'F' 'F' 'M' 'M' 'F' 'M' 'F' 'F' 'M' 'F' 'F']\n",
        "Counter({'F': 9, 'M': 4})\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The code above shows how to use a random permutation and the first 13 slots in the list to indicate the survivors in that permutation. Then, all you have to do is count the number of males and females in the first 13 slots. To get all ppossible permutations counted and divided this way, we can use a third-party combinatorics module as shown in the code  below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "foo = lambda i: len(set(range(10)) & set( i[0] )) # count males in first group of 10 males total\n",
      "o=[foo(i) for i in combinatorics.labeled_balls_in_unlabeled_boxes(24,[13,11]) ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(o,10,align='left')\n",
      "title('Surviving males under $H_0$')\n",
      "xlabel('number of surviving males')\n",
      "axis(xmin=0);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oySIiIholWURERKMki4iIaNTzyULSXEn3SVon6QPdjmdXmTx5KpK6/oiIGE5P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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x76a8af0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# probability of observing 9 male survivors under H_0 is the following\n",
      "co=Counter(o)\n",
      "print 'p-value= ',(co[9]+co[10])/sum(co.values())\n",
      "print 'p-value= ',(co[0]+co[1]+co[2]+co[9]+co[10])/sum(co.values())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-value=  0.00415601023018\n",
        "p-value=  0.0110883025979\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#using one-way chi-squared proportion test\n",
      "from scipy import stats\n",
      "print stats.chisquare( [9,4],[6.5,6.5])\n",
      "print stats.fisher_exact(df.values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1.9230769230769231, 0.16551785869746993)\n",
        "(22.5, 0.0045261811818548964)\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}